List of Publications

• Sparse Representations and Approximation Theory, Journal of Approximation Theory 163 (2011), 388-412 [[pdf]]. This article may be viewed at Science Direct.
• (edited with A. Kroó and Y. Xu) In Memoriam Borislav D. Bojanov: 18 November 1944–8 April 2009, Journal of Approximation Theory 162 (2010), 1739-1765 [[pdf]]. This article may be viewed at Science Direct.
• (with R. Pinchasi) Dominating Subsets under Projections, SIAM J. Discrete Math. 24 (2010), 910–920 [[pdf]]. This article may be viewed directly from SIDMA. Review from Zentralblatt.
• (with A. Kroó) Strong Uniqueness, Surveys in Approximation Theory 5 (2010), 1-91. [[pdf], [ps]] and Surveys in Approximation Theory. Review from MR.
• Zero Minors of Totally Positive Matrices, Electronic Journal in Linear Algebra 17 (2008), 532-542. [[pdf]]. This article may be viewed directly from ELA.
• (with D. Hershkowitz) On Nonnegative Sign Equivalent and Sign Similar Factorizations of Matrices, Electronic Journal in Linear Algebra 16 (2007), 162-170. [[pdf], [ps]]. This article may be viewed directly from ELA. Review from Zentralblatt.
• (with D. Wulbert) Extending n-Convex Functions, Studia Math. 171 (2005), 125-152. [[pdf]]. Review from MR.
• (with E. L. Ortiz) Herman Müntz: A Mathematician's Odyssey, Mathematical Intelligencer 27 (2005), 22-31. [[pdf]]. Review from Zentralblatt.
• Density in Approximation Theory, Surveys in Approximation Theory 1 (2005), 1-45. [[pdf], [ps]] and Surveys in Approximation Theory. Review from MR. Review from Zentralblatt.
• Strictly Hermitian Positive Definite Functions, Journal d'Analyse Math. 94 (2004), 293-318. [[pdf], [ps]].
• Interpolation by Matrices, Electronic Journal in Linear Algebra 11 (2004), 281-291. [[pdf], [ps]]. This article may be viewed directly from ELA. Review from Zentralblatt
• Density Methods and Results in Approximation Theory, Orlicz Centenary Volume, Banach Center Publications, Volume 64, Z. Ciesielski, A. Pelczynski, L. Skrzypczak (eds.), 173-192, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2004. [[pdf], [ps]].
• Strictly Positive Definite Functions on a Real Inner Product Space, Advances in Computational Mathematics 20 (2004), 263-271. [[pdf], [ps]]. This article may be viewed at Kluwer Online. Review from MR.
• (with C. de Boor) The B-spline Recurrence Relations of Chakalov and Popoviciu, Journal of Approximation Theory 124 (2003), 115-123. [[pdf], [ps]]. This article may be viewed at Science Direct. Review from Zentralblatt.
• Negative Theorems in Approximation Theory, American Math. Monthly 110 (2003), 900-911. [[pdf], [ps]]. Some corrections regarding this paper are in this file. Review from MR. Review from Zentralblatt.
• (with A. Atzmon) Rank Restricting Functions, Linear Algebra and its Applications 372 (2003), 305-323. [[pdf], [ps]]. This article may be viewed at Science Direct. Review from Zentralblatt.
• (with Uri Elias) Non-Linear Eigenvalue-Eigenvector Problems for STP Matrices, Proceedings of the Royal Society of Edinburgh: Section A 132 (2002), 1307-1331. [[pdf], [ps]]. Reviews from Zentralblatt and from MR.
• (with Uri Elias) Non-Linear Eigenvalue Problems for a Class of Ordinary Differential Equations, Proceedings of the Royal Society of Edinburgh: Section A 132 (2002), 1333-1359. [[pdf], [ps]]. Reviews from Zentralblatt and from MR.
• Some Remarks on Zero-Increasing Transformations, Approximation Theory X: Abstract and Classical Analysis, C. K. Chui, L. L. Schumaker, J. Stoeckler (eds.), 333-352, Vanderbilt Univ. Press., Nashville, 2002. [[pdf], [ps]]. Review from MR.
• (with J. M. Carnicer and J. M. Pena) On some Zero-Increasing Operators, Acta Math. Hungar. 94 (2002), 173-190. [[pdf], [ps]]. Reviews from Zentralblatt and from MR.
• (with J. M. Carnicer and J. M. Pena) On Zero-Preserving Linear Transformations, Journal of Mathematical Analysis and Applications 266 (2002), 237-258. [[pdf], [ps]]. This article may be viewed at Science Direct.
• Weierstrass and Approximation Theory, Journal of Approximation Theory 107 (2000), 1-66. [[pdf], [ps]]. This article may be viewed at Science Direct. Some additions/corrections regarding this paper are in this file. Reviews from Zentralblatt and from MR.
• On a Problem of G. G. Lorentz, Journal of Approximation Theory 103 (2000), 29-54. [[pdf], [ps]]. This article may be viewed at Science Direct. Some additional comments on this paper are here. Reviews from Zentralblatt and from MR.
• Approximation Theory of the MLP Model in Neural Networks, Acta Numerica 8 (1999), 143-196. [[pdf], [[ps]]. Review from MR.
• (with Vitaly Maiorov) Lower Bounds for Approximation by MLP Neural Networks, Neurocomputing 25 (1999), 81-91. [[pdf], [ps]].
• (with Martin D. Buhmann) Identifying Linear Combinations of Ridge Functions, Adv. in Applied Math. 22 (1999), 103-118. [[pdf], [ps]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR.
• An Interlacing Property of Eigenvalues of Strictly Totally Positive Matrices, Linear Algebra and its Applications 279 (1998), 201-206. [[pdf], [ps]]. This article may be viewed at Science Direct. Review from MR.
• Uniqueness of Smoothest Interpolants, East Journal of Approximation 3 (1997), 377-380. [[pdf], [ps]]. Review from Zentralblatt.
• Approximating by Ridge Functions, in Surface Fitting and Multiresolution Methods, A. Le Mehaute, C. Rabut, L. L. Schumaker (eds.), pp. 279-292, Vanderbilt University press, Nashville, 1997. [[pdf]], [[ps]]. Review from MR.
• (with Oleg Davydov) Best Approximation and Cyclic Variation Diminishing Kernels, Journal of Approximation Theory 89 (1997), 380-423. [[pdf], [ps]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR.
• (with Martin Buhmann) On a Recovery Problem, Annals of Numerical Mathematics 4 (1997), 129-142. The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin. [[pdf], [ps]]. Reviews from Zentralblatt and from MR.
• TDI-Subspaces of C(R^d) and Some Density Problems from Neural Networks, Journal of Approximation Theory 85 (1996), 269-287. [[pdf], [ps]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR.
• Spectral Properties of Totally Positive Kernels and Matrices, in Total Positivity and its Applications, M. Gasca, C. A. Micchelli (eds.), pp. 477-511, Kluwer Academic Publishers, 1996. [[pdf], [ps]].
• Some Density Problems in Multivariate Approximation, in Approximation Theory: Proceedings of the International Dortmund Meeting IDOMAT 95, M. W. Muller, M. Felten, D. H. Mache (eds.), pp. 277-284, Akademie Verlag, 1995. [[pdf], [ps]]. Review from Zentralblatt.
• (with B. Wajnryb) A Problem of Approximation Using Multivariate Polynomials, Uspekhi Mat. Nauk 50 (1995), 89-110, (in Russian) = Russian Math. Surveys 50 (1995), 319--340 (in English). [[pdf], [ps]]. Reviews from Zentralblatt and from MR.
• (with B. Wajnryb) Multivariate Polynomials: A Spanning Question, Constructive Approximation 11 (1995), 165-180. [[pdf], [ps]]. Review from MR.
• (with C. H. FitzGerald and C. A. Micchelli) Functions that Preserve Families of Positive Semidefinite Matrices, Lin. Alg. and Appl. 221 (1995), 83-102. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR.
• (with V. Ya. Lin) Approximation of Multivariate Functions, in Advances in Computational Mathematics, H. P. Dikshit, C. A. Micchelli (eds.), pp. 257-266, World Scientific, 1994. [[pdf], [ps]].
• (with C. A. Micchelli) Variational Problems Arising from Balancing Several Error Criteria, Rendiconti di Matematica 14 (1994), 37-86. [[pdf]]. This article may be viewed at Rendiconti di Matematica. Reviews from Zentralblatt and from MR.
• (with V. Ya. Lin) Fundamentality of Ridge Functions, Journal of Approximation Theory 75 (1993), 295-311. [[pdf], [ps]]. This article may be viewed at Science Direct. Review from Zentralblatt.
• (with D. Braess) Interpolation by Ridge Functions, Journal of Approximation Theory 73 (1993), 218-236. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR.
• (with M. Leshno, V. Ya. Lin and S. Schocken) Multilayer Feedforward Networks with a Non-Polynomial Activation Function can Approximate any Function, Neural Networks 6 (1993), 861-867. [[pdf]].
• Uniqueness in Vector-Valued Approximation, Journal of Approximation Theory 73 (1993), 17-92. [[pdf]]. This article may be viewed at Science Direct. Reviews from Zentralblatt and from MR.
• (with D. Wulbert) The Multi-Dimensional Van Neumann Alternating Direction Search Algorithm in C(B) and L¹, Journal of Functional Analysis 104 (1992), 121-148. [[pdf]]. Reviews from Zentralblatt and from MR.
• (with C. A. Micchelli) Descartes Systems from Corner Cutting, Constructive Approximation 7 (1991), 161-194. [[pdf]].
• (with H. Strauss) L¹–Approximation with Constraints, Transactions of the American Mathematical Society 322 (1990), 239-261. [[pdf]]. This article may be viewed at JSTOR. Reviews from Zentralblatt and from MR.
• (with L. Elsner and D. Hershkowitz) Functional Inequalities for Spectral Radii of Non-Negative Matrices, Linear Algebra and its Applications 129 (1990), 103-130. [[pdf]]. Reviews from Zentralblatt and from MR.
• (with C. A. Micchelli) Some remarks on nonnegative polynomials on polyhedra. Probability, Statistics, and Mathematics: Papers in honor of Samuel Karlin, 163-186, Academic Press, Boston, MA, 1989. [[pdf]]. Reviews from Zentralblatt and MR.
• (with H. Strauss) Best Approximation with Coefficient Constraints, IMA Journal of Numerical Analysis 8 (1988), 1-22. [[pdf]]. Review from Zentralblatt.
• (with B. Wajnryb) Necessary Conditions for Uniqueness in L¹–Approximation, Journal of Approximation Theory 53 (1988), 54-66. [[pdf]]. Reviews from Zentralblatt and MR.
• Continuous Selections for the Metric Projection on C₁, Constructive Approximation 4 (1988), 85-96. [[pdf]]. Reviews from Zentralblatt and MR.
• On Smoothest Interpolants, SIAM Journal of Mathematical Analysis 19 (1988), 1431-1441. [[pdf]]. Review from MR.
• (with H. Strauss) One-Sided L¹–Approximation to Differentiable Functions, Approximation Theory and its Applications 3 (1987), 81-96. [[pdf]]. Review from MR.
• (with V. Totik) One-Sided L¹–Approximation, Canadian Mathematical Bulletin 29 (1986), 84-90. [[pdf]]. Reviewsfrom Zentralblatt and MR.
• Unicity Subspaces in L¹–Approximation, Journal of Approximation Theory 48 (1986), 226-250. [[pdf]]. Review from MR.
• n-Widths and Optimal Recovery, Proceedings of Symposia in Applied Mathematics, Vol. 36, Ed., C. de Boor, 51-66, American Mathematics Society, Providence, 1986. [[pdf]].
• (with J. M. Anderson, P. Erdös and O. Shisha) The Closed Linear Span of {x^k-c_k}₁^∞, Journal of Approximation Theory 43 (1985), 75-80. [[pdf]]. Reviews from Zentralblatt and MR.
• n–Widths of Sobolev Spaces in L^p, Constructive Approximation 1 (1985), 15-62. [[pdf]]. Review from MR.
• Some Extremal Problems for Strictly Totally Positive Matrices, Linear Algebra and its Applications 64 (1985), 141-156. [[pdf]]. Reviews from Zentralblatt and MR.
• n-Widths in Approximation Theory: A Survey, Approximation Theory IV, Eds., C. K. Chui, L. L. Schumaker, J. D. Ward, 153-186, Academic press, N. Y., 1983. [[pdf]].
• (with G. J. O. Jameson) Positive and Minimal Projections in Function Spaces, Journal of Approximation Theory 37 (1983), 182-195. [[pdf]]. Review from MR.
• (with O. Shisha) A Variation on the Chebyshev Theory of Best Approximation, Constructive Function Theory, 81, 479-481, Sofia, 1983. [[pdf]]. Review from Zentralblatt.
• (with C. de Boor and S. Friedland) Inverses of Infinite Sign Regular Matrices, Transactions of the American Mathematics Society 274 (1982), 59-68. [[pdf]]. Review from MR.
• (with C. de Boor) The Approximation of a Totally Positive Band Matrix by Strictly Totally Positive One, Linear Algebra and its Applications 42 (1982), 81-98. [[pdf]].
• (with C. de Boor and R. Q. Jia) Structure of Invertible (Bi)-infinite Totally Positive Matrices, Linear Algebra and its Applications 47 (1982), 41-55. [[pdf]].
• (with O. Shisha) Variations on the Chebyshev and L^q Theories of Best Approximation, Journal of Approximation Theory 35 (1982), 148-168. [[pdf]]. Reviews from Zentralblatt and MR.
• Best Approximations by Smooth Functions, Journal of Approximation Theory 33 (1981), 147-178. [[pdf]]. Review from MR.
• Bernstein's Comparison Theorem and a Problem of Braess, Aequationes Mathematicae 23 (1981), 98-107. [[pdf]]. Reviews from Zentralblatt and MR.
• (with C. A. Micchelli) On n-Widths in L^∞, II: Some related extremal problems, Constructive Function Theory, 77, 403-416, Sofia, 1980. [[pdf]].
• (with L. Brutman) On the Erdos Conjecture concerning Minimal Norm Interpolation on the Unit Circle, SIAM Journal of Numerical Analysis 17 (1980), 373-375. [[pdf]]. Review from MR.
• (with Z. Ziegler) Interlacing Properties of the Zeros of the Error Functions in Best L^p Approximation, Journal of Approximation Theory 27 (1979), 1-18. [[pdf]]. Review from MR.
• On n-Widths of Periodic Functions, Journal d'Analyse Mathematique 35 (1979), 209-235. [[pdf]]. Review from MR.
• Matrices and n-Widths, Linear Algebra and its Applications 27 (1979), 245-278. [[pdf]]. Review from MR.
• (with C. A. Micchelli) The n-Widths of Rank n+1 Kernels, Journal of Integral Equations 1 (1979), 111-130. [[pdf]].
• (with J. W. Lee) Spectral Properties and Oscillation Theorems for Mixed Boundary-Value Problems of Sturm-Liouville Type, Journal of Differntial Equations 27 (1978), 190-213. [[pdf]]. Review from MR.
• (with C. A. Micchelli) Some Problems in the Approximation of Functions of Two Variables and n-Widths of Integral Operators, Journal of Approximation Theory 24 (1978), 51-77. [[pdf]]. Review from MR.
• (with C. de Boor) Proof of the Conjecture of Bernstein and Erdos concerning the Optimal Nodes for Polynomial Interpolation, Journal of Approximation Theory 24 (1978), 289-303. [[pdf]]. Review from MR.
• Some Extremal Problems of Perfect Splines and the Pointwise Landau Problem on the Finite Interval, Journal of Approximation Theory 23 (1978), 37-64. [[pdf]]. Review from MR.
• (with C. A. Micchelli) Moment Theory for Weak Chebyshev Systems with Applications to Monosplines, Quadrature Formulae and Best One-Sided L¹ Approximation by Spline Functions with Fixed Knots, SIAM Journal of Mathematical Analysis 8 (1977), 206-230. [[pdf]]. Review from MR.
• (with C. A. Micchelli) On n-Widths in L^∞, Transactions of the American Mathematics Society 234 (1977), 139-174. [[pdf]]. Review from MR.
• (with C. A. Micchelli) Total Positivity and the Exact n-Width of Certain Sets in L¹, Pacific Journal of Mathematics 71 (1977), 499-515. [[pdf]]. Review from MR.
• (with C. A. Micchelli) On a Best Estimator for the Class M^r using only Function Values, Indiana University Mathematics Journal 26 (1977), 751-759. [[pdf]]. Review from MR.
• (with C. A. Micchelli) Best Mean Approximation to a 2-dimensional Kernel by Tensor Products, Bulletin of the American Mathematical Society 83 (1977), 400-402. [[pdf]]. Review from MR.
• (with C. de Boor) Backward Error Analysis for Totally Positive Linear Systems, Numerische Mathematik 27 (1977), 485-490. [[pdf]]. Review from MR.
• One-Sided L¹-Approximation by Splines with Fixed Knots, Journal of Approximation Theory 18 (1976), 130-135. [[pdf]].
• A Simple Proof of the Hobby-Rice Theorem, Proceedings of the American Mathematics Society 60 (1976), 82-84. [[pdf]]. Review from MR.
• (with C. A. Micchelli) On n-Widths and Optimal Recovery in M^r, Approximation Theory, II, Eds., G. G. Lorentz, C. K. Chui, L. L. Schumaker, 475-478, Academic Press, N. Y., 1976.[[pdf]]. Review from MR.
• (with C. A. Micchelli) The Exact Asymptotic Value for the n-Width of Smooth Functions in L^∞, Approximation Theory, II, Eds., G. G. Lorentz, C. K. Chui, L. L. Schumaker, 469-474, Academic Press, N. Y., 1976. [[pdf]]. Review from MR.
• (with S. Karlin) Divided Differences and other Non-linear Existence Problems at Extremal Points, in Studies in Spline Functions and Approximation Theory, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 327-352, Academic Press, N. Y., 1976. [[pdf]].
• (with S. Karlin) Interpolation by Splines with Mixed Boundary Conditions, in Studies in Spline Functions and Approximation Theory, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 305-325, Academic Press, N. Y., 1976. [[pdf]].
• (with S. Karlin) An Extremal Problem of Multiple Gaussian Nodes, in Studies in Spline Functions and Approximation Theory, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 143-162, Academic Press, N. Y., 1976.[[pdf]].
• (with S. Karlin) Gaussian Quadrature Formulae with Multiple Nodes, in Studies in Spline Functions and Approximation Theory, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 113-141, Academic Press, N. Y., 1976. [[pdf]].
• Applications of Representation Theorems to problems of Chebyshev Approximation with Constraints, in Studies in Spline Functions and Approximation Theory, S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, 83-111, Academic Press, N. Y., 1976. [[pdf]].
• Asymptotic Minimum Norm Quadrature Formulae, Numerische Mathematik 24 (1975), 163-175. [[pdf]].
• Representation Theorems for Tchebycheffian Polynomials with Boundary Conditions and their Applications, Israel Journal of Mathematics 17 (1974), 11-34. [[pdf]]. Review from MR.
• (with S. Karlin) Oscillation Properties of Generalized Characteristic Polynomials for Totally Positive and Positive Definite Matrices, Linear Algebra and its Applications 8 (1974), 281-312. [[pdf]]. Review from MR.

Books

• A. Pinkus, Totally Positive Matrices, Cambridge University Press, 2010. Here is the Table of Contents and Foreword. You can also see the Afterword, References and Indices. Review in MR. Review in Zentralblatt.
• F. Cucker, A. Pinkus, M. J. Todd, (editors) Foundations of Computational Mathematics, Hong Kong 2008, London Mathematical Society Lecture Note Series 363, Cambridge University Press, 286 pages, 2009. Details from CUP.
• L. M. Pardo, A. Pinkus, E. Suli, M. J. Todd, (editors) Foundations of Computational Mathematics, Santander 2005, London Mathematical Society Lecture Note Series 331, Cambridge University Press, 394 pages, 2006. Details from CUP.
• N. Dyn, D. Leviatan, D. Levin, A. Pinkus, (editors) Multivariate Approximation and Applications, Cambridge University Press, 284 pages, 2001. Details can be seen here.
• A. Pinkus, S. Zafrany, Fourier Series and Integral Transforms, Cambridge University Press, 189 pages, 1997. For some information concerning this textbook, see here.
• S. Zafrany, A. Pinkus, Fourier Series and Integral Transforms, Michlol, 182 pages, 1995. Teaching Textbook in Hebrew. Available from the Michlol bookstore in the Technion.
• P. Nevai, A. Pinkus, (editors) Progress in Approximation Theory, Academic Press, 1991.
• A. M. Pinkus, On L¹–Approximation, Cambridge Tracts in Mathematics, Cambridge University Press, Vol. 93, 239 pages, 1989. Reviews from Zentralblatt and MR. The book is still available here.
• A. Pinkus, n–Widths in Approximation Theory, Ergebnisse, Springer-Verlag, 291 pages, 1985. Reviews from Zentralblatt and MR. A list of some errata.
• S. Karlin, C. A. Micchelli, A. Pinkus, I. J. Schoenberg, Studies in Spline Functions and Approximation Theory, Academic Press, N. Y., 1976. (A collection of papers by the four authors.)